Let $\mathbf { r } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and $r = | \mathbf { r } |$.
Find $\nabla \cdot ( 6 \mathbf { r } )$
Select the correct answer.
A) 6
B) 12
C) 18
D) 30
E) None of these

Question

Quizplus · Accepted Answer

The divergence of a vector field $\mathbf{F} = f(x, y, z) \mathbf{i} + g(x, y, z) \mathbf{j} + h(x, y, z) \mathbf{k}$ is given by $\nabla \cdot \mathbf{F} = \frac{\partial f}{\partial x} + \frac{\partial g}{\partial y} + \frac{\partial h}{\partial z}$. For $\mathbf{F} = 6\mathbf{r} = 6x \mathbf{i} + 6y \mathbf{j} + 6z \mathbf{k}$, the divergence is $6 \cdot 1 + 6 \cdot 1 + 6 \cdot 1 = 18$.

Let r=xi+yj+zk\mathbf { r } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }r=xi+yj+zk

Let $\mathbf { r } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$